Comparison of Over-damped Pipe Flow LES and Sparially Filtered DNS

Abstract

While near-wall streaks in turbulent shear flows have been shown to regenerate themselves in an autonomous self-sustained process and their dynamics are well captured by only a handful of exact coherent solutions (ECS) of the Navier-Stokes equations, the origin and the dynamics of very large scale motions (VLSM) is more controversial. One major obstacle in extending dynamical systems approaches from transitional range to high Reynolds number shear flows in order to compute a small set of ECS which form the skeleton of VLSM is the presence of a much broader spectrum of turbulent length scales. Following the approach used in Rawat et al. we aim to use large eddy simulation (LES) techniques with a simple but robust Smagorinsky model to isolate VLSM in a turbulent pipe flow by quenching all significantly smaller motions with an unphisically high value of the model constant Cs . The results from our over-damped LES will eventually show whether VLSM are self-sustained or rather depend on the near-wall cycle. They will further provide proper initial conditions from which VLSM related ECS can be converged. At the colloquium we will present and discuss first LES results for a moderately high Reynolds number of Re ≈ 60 000 and discuss the effect of different levels of artificially increased turbulent viscosity (Cs) and its impact on turbulence statistics and energy spectra. Figure 1 exemplarily shows mean and rms profiles for different Re and different Cs. The LES results will also be compared to results from a direct numerical simulation (DNS) at the same Reynolds number. Applying different spectral filters (1d, 2d, high-pass, low-pass) with different cut-off wave numbers to the DNS data will further allow us to relate the mpact of Cs on statistics and spectra with different length scales in the flow field. Details and origin of the used numerical methods are describe in detail in Ashley (LES), Feldmann et al. (DNS), and reference therein.